Two small children, Daniel and Christine, were playing a game to see who would be the first to reach the door. The children started the game by standing 20 meters away from the door, and then they each alternated doing the following:

i. Daniel moved one-half the distance between himself and the door on each move.

ii. Christine moved 1 meter toward the door on each move.

(a) How far was each child from the door after the first move?

(b) After four moves, was Daniel or Christine closer to the door? Show your work.

(c) Daniel thought that the game was unfair because he would never reach the door. Explain why his statement is correct or incorrect.

The $50-\text{mm}$-diameter steel $(G=80\ \mathrm{GPa})$ shaft shown in given figure is fixed to rigid walls at both ends. When a torque of $4.75\ \mathrm{kN} \cdot \mathrm{m}$ is applied as shown, find (a) The maximum shearing stress in the shaft. (b) The angle of rotation of the section where the torque is applied with respect to its no load position.

A point source with volume flow Q = 30 m³/s is immersed in a uniform stream of speed 4 m/s. A Rankine half-body of revolution results. Compute (a) the distance from source to the stagnation point and (b) the two points (r, θ) on the body surface where the local velocity equals 4.5 m/s.

Using conversion factors, solve the following clinical problem: A nurse practitioner prepares 500. mL of an IV of normal saline solution to be delivered at a rate of 80. mL/h. What is the infusion time, in hours, to deliver 500. mL?

A person opens a door by applying a 15-N force perpendicular to it at a distance 0.90 m from the hinges. The door is pushed wide open (to $120^{\circ})$ in 2.0 s. (a) How much work was done? (b) What was the average power delivered?

The table lists the measurements of a lot bounded by a stream and two straight roads that meet at right angles, where x and y are measured in feet.

Use the model in part (a) to estimate the area of the lot.

Explain why you cannot cool your kitchen by leaving your refrigerator door open on a hot day. (Why does turning on a room air conditioner cool down the room, but opening a refrigerator door does not?)

A 5-cm-diameter horizontal jet of water with a velocity of 40 m/s relative to the ground strikes a flat plate that is moving in the same direction as the jet at a velocity of 10 m/s. The water splatters in all directions in the plane of the plate. How much force does the water stream exert on the plate?

"Suppose the snark population on Citsigol Island is currently 3,400 and growing at a rate of 18% per year.

a. Write a recursive definition for the sequence $P$ of snark populations $n$ years from now (assuming an unlimited growth model).

b. Write an explicit formula for the population $P$ of snarks $n$ years from now (assuming an unlimited growth model).

c. If the snark population is modeled with the limited growth model difference equation $P_{n+1}=P_n+0.18 P_n\left(1-\frac{P_n}{17000}\right)$, what is the end behavior of the sequence $P$ ? What does the end behavior mean in this situation?"

Will two limp pieces of paper held a few inches apart come closer together or move farther apart if you blow between them? Explain.\s* Q31. A gust of wind blows sideways across an open outward-swinging door. Will the door slam shut or swing open as a result of this? Explain.

Suppose that the force is applied perpendicular to the torque arm. Given: $\tau=35.7\ \mathrm{lb}\ \mathrm{ft}$ $r=0.0240 \mathrm{ft}$

$$F= ?$$

If you leave me refrigerator door open and the refrigerator runs continuously, does the kitchen get colder or warmer? Explain.

In the earlier example given, was treated the merry-go-round plus child as a system (shown in the given figure) whose angular momentum is conserved. The merry-go-round is initially at rest, so its initial angular momentum is zero, but at the end it is rotating, so its final angular momentum is nonzero. The angular momentum of the merry-go-round alone thus changes, which can only happen if there is a torque on the merry-go-round. What force provides this torque?

(a) The force of gravity on the merry-go-round

(b) The force of air drag on the merry-go-round

(c) The force produced by the child when she jumps off

(d) The force of friction at the axle of the merry-go-round

A soccer player $20.0 \mathrm{~m}$ from the goal stands ready to score. In the way stands a goalkeeper, $1.70 \mathrm{~m}$ tall and $5.00 \mathrm{~m}$ out from the goal, whose crossbar is at $2.44 \mathrm{~m}$ high. The striker kicks the ball toward the goal at $18 \mathrm{~m} / \mathrm{s}$. Determine whether the ball makes it over the goalkeeper and/or over the goal for each of the following launch angles (above the horizontal): (c) $30^{\circ}$.